##### Department of Mathematics,

University of California San Diego

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### Center for Computational Mathematics Seminar

## Antonio Palacios

#### San Diego State University

## Complex Networks: Connecting Equivariant Bifurcation Theory with Engineering Applications

##### Abstract:

The advent of novel engineered or smart materials, whose properties can be significantly altered in a controlled fashion by external stimuli, has stimulated the design and fabrication of smaller, faster, and more energy-efficient devices. As the need for even more powerful technologies grows, networks have become popular alternatives to advance the fundamental limits of performance of individual devices. Thus, in the first part of this talk we provide an overview of fifteen years of work aimed at combining ideas and methods from equivariant bifurcation theory to model, analyze and fabricate novel technologies such as: ultra-sensitive magnetic and electric field sensors; networks of nano oscillators; and multi-frequency converters. In the second part of the talk, we discuss more recent work on networks of vibratory gyroscopes systems. Under normal conditions of operation, the model equations can be reformulated in a Hamiltonian structure and the corresponding normal forms are then derived. Through a normal form analysis, we investigate the effects of various coupling topologies and unravel the nature of the bifurcations that lead a ring of gyroscopes of any size into and out of synchronization. The synchronization state is particularly important because it can lead to a significant reduction in phase drift, thus enhancing performance. The Hamiltonian approach can, in principle, be readily extended to other symmetry related systems.

Host: Melvin Leok

### November 17, 2015

### 10:00 AM

### AP&M 2402

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